Robustness Comparison of Exponentially Weighted Moving-Average Charts on Autocorrelated Data and on Residuals

Abstract

Control charting of autocorrelated data has been the subject of extensive research over the past two decades. A standard approach is to apply an exponentially weighted moving average (EWMA) chart to either the autocorrelated data or to the residuals of an autoregressive moving-average (ARMA) model of the process. Numerous empirical studies have demonstrated that many control charts for autocorrelated data, residual-based charts in particular, lack robustness to ARMA modeling errors. In this article, we quantify and corroborate these empirical findings by developing analytical expressions for the sensitivity of EWMA control charts applied to residuals and to autocorrelated data. The analytical results provide insight into the mechanisms behind the (lack of) robustness and also provide a basis for comparing the robustness of the two approaches. One conclusion is that, although the residual-based EWMA may lack robustness, it is generally more robust than the EWMA applied to the autocorrelated data.